Question

Henry decides to start an investment savings account. He initially deposits $500 dollars to the bank. Every year, Henry's bank account increases by 15%. Assume x represents the number of years and y is the amount of money in the bank. Which function models this situation below?

Answer 1

`y= 500(1+0.15)^x`

Explanation:

This problem can be solved using concept of compound interest

In compound interest

if p is the principal amount

and r is the interest rate

then value of principal amount(A) after n years time is given by

A = p(1+r)^n

=>
`A = p(1+r)^n`

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in the problem

in place of n we have x years

y is the amount which is the total amount after n years

p is the principal money deposited = $500

r = 15%

substituting these value in the formula for amount after n years we have

`y= 500(1+15/100)^x\\y= 500(1+0.15)^x`

Thus, function modeling the situation is
`y= 500(1+0.15)^x`